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REVIEW 3 major objections 4 minor 72 references

Secure Integrated Sensing and Communication Networks: Stochastic Performance Analysis

T0 review · 3 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read This paper claims that the stochastic security and sensing performance of a random MIMO ISAC downlink reduces to closed-form expressions for two secure precoders, and that these expressions trace the full CRB–secrecy-rate boundary.

desk verdict The exact secrecy-rate results are solid and the model combination is new, but the headline 'ergodic CRB' is a truncated proxy that diverges under the stated angle model, so the tradeoff plots need re-flagging before the paper is fully trusted. read the letter →

arxiv 2507.23234 v2 pith:A7GFNU3V submitted 2025-07-31 cs.IT eess.SPmath.IT

Marziyeh Soltani , Mahtab Mirmohseni , Rahim Tafazolli This is my paper · ORCID
classification cs.ITeess.SPmath.IT MSC 94A1594A12
keywords integratedsensingandcommunicationISACphysicallayersecurityergodicsecrecyrateCramér–Raoboundprivacystochasticperformanceanalysisbeamforming
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper tries to establish that the security and sensing performance of a random MIMO integrated sensing and communication (ISAC) downlink can be reduced to closed-form expressions, despite random Rayleigh fading, a uniformly random target angle, and three kinds of adversaries. The setting is one base station that simultaneously serves a single-antenna user, estimates a target's azimuth angle from its radar echo, and defends against a passive communication eavesdropper, a strong or weak multi-antenna sensing eavesdropper, and possibly a target that itself acts as an eavesdropper. For two structured precoders, SSJB and SLB, the paper derives the ergodic secrecy rate, the ergodic Cramér–Rao bound (CRB) for angle estimation at both the base station and the sensing eavesdropper, and the outage probability that the CRB exceeds a threshold. If the analysis is correct, these metrics, together with the three tradeoffs the paper identifies between sensing accuracy, secure rate, and sensing privacy, become computable from a handful of formulas and a single three-dimensional Gaussian integral, with no iterative optimization.

What carries the argument

The load-bearing object is the trivariate Gaussian approximation of the channel sums. For $(R, T, K)$, the real part, imaginary part, and power sum of the randomized beam-channel terms, Lemma 16 fixes $\mu_d = [0,0,1]^T$ and $\Sigma_d = \operatorname{diag}(1/2, 1/2, 1)$, giving $(R,T,K) \to \mathcal{N}_3(N\mu_d, N\Sigma_d)$ for large $N$; Appendix F then replaces $S = R^2 + T^2$ by an $N\cdot\mathrm{Exp}(1)$ variable independent of $K \sim \mathcal{N}(N,N)$. This single approximation converts every CRB and rate expression into an integral against a Gaussian density. The two precoders are the second piece of machinery: SSJB sends user data along a vector $t_1 = \alpha \tilde{a} + \beta \tilde{h}$ in the span of the target steering direction and the user channel, with artificial noise in the null space, while SLB splits power among the user direction $h/\|h\|$, the steering direction $a/\|a\|$, its derivative $a'/\|a'\|$, and artificial noise. Lemma 1 fixes the construction of the secure sensing part: the beamformer minimizing $\mathrm{CRB}(\theta) - \mathrm{CRB}(\varphi)$ lies in the span of $a$ and $a'$.

What would settle it

Compute the paper's metrics without the Gaussian step: for the same parameters (for instance $N = 15$, $M = 17$, $N_e = 15$), evaluate the ergodic secrecy rate, $E[\mathrm{CRB}(\theta)]$, and $P(\mathrm{CRB} > \varepsilon)$ by Monte Carlo over the exact Rayleigh fading and uniform angle distributions, and compare against the closed forms. The precise weak spot to probe is the independence of $S = R^2 + T^2$ and $K$, whose true correlation is $1/\sqrt{N}$; repeat the comparison at $N = 4, 9, 16, 25$ and locate the smallest $N$ at which the closed forms leave the Monte Carlo confidence band — if that $N$ lies at or above the operating array size, the central claim fails at that operating point.

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Extended reading notes

Core claim

The paper's central claim is that for a Rayleigh-fading MIMO ISAC downlink with uniformly distributed target azimuth, the security and privacy performance of two closed-form precoders, SSJB and SLB, is captured by a small set of analytic metrics: the ergodic secrecy rate, the ergodic Cramér–Rao bound (CRB) for target localization at the base station and at strong and weak sensing eavesdroppers, and outage probabilities of the form $P(\mathrm{CRB} > \varepsilon)$. The analytic engine is the multidimensional central limit theorem applied to $(R, T, K) = (\mathrm{Re}\sum_i e^{j f_i} h_i, \mathrm{Im}\sum_i e^{j f_i} h_i, \sum_i |h_i|^2)$, which the paper treats as trivariate normal with mean $N[0,0,1]^T$ and covariance $N\operatorname{diag}(1/2,1/2,1)$, so that $S = R^2 + T^2$ behaves as $N\cdot\mathrm{Exp}(1)$, independent of $K$. On this foundation the paper derives exact results such as the external eavesdropper's ergodic rate $\int_0^\infty e^{-T/(2C_1)}(1 + T C_2/C_1)^{-(N-2)}\,dt$ and the malicious-target leakage $\log(1 + P\tau |c_5|^2 |\alpha|^2 N / \sigma_t^2)$, and from them traces the boundary of the CRB–secrecy-rate region. The boundary exposes three tradeoffs: sensing accuracy versus communication rate, sensing accuracy versus secure communication rate, and communication security versus sensing privacy.

Load-bearing premise

Everything rests on treating the three channel-derived quantities $(R, T, K)$ as jointly Gaussian with $S = R^2 + T^2$ effectively independent of $K$; that is only asymptotically true, since the true $S$ and $K$ are correlated, and if the approximation is inaccurate at the antenna count of interest, every closed-form metric and tradeoff boundary inherits the error.

Editorial extensions

If this is right

  • Under the two precoders, the ergodic secrecy rate, ergodic CRB, and CRB outage probability come out in closed form or as tight bounds, so evaluating security and privacy in random ISAC no longer requires iterative non-convex optimization.
  • The CRB–secrecy-rate boundary gives designers a quantitative statement of three tradeoffs — sensing accuracy versus rate, sensing accuracy versus secure rate, and communication security versus sensing privacy — so the cost of a secrecy target can be read off directly as a loss in estimation accuracy.
  • SSJB can place user data orthogonal to the target direction, so it can drive malicious-target leakage to zero and is the more resilient scheme against malicious targets; SLB aligns with the user channel and therefore achieves higher rates and stronger protection against external eavesdroppers.
  • The secure-sensing-optimal beamformer provably lies in the span of the steering vector and its angle-derivative, so SLB's construction is supported by a structural lemma rather than chosen ad hoc.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Editorial inference: because Lemma 16 makes the Gaussian law of $(R,T,K)$ independent of the target angle, the same machinery should extend to other angle distributions and, with additional steering directions, to multiple targets; the open question is whether the derived bounds stay tight in those regimes.
  • Editorial inference: Lemma 12's exact leakage formula shows malicious-target leakage is controlled entirely by the power split $\tau$ and the projection weight $\alpha$; this is a concrete, testable design relationship that a hardware experiment could verify by measuring the target's decoded SINR against $\tau$.
  • Editorial inference: since the true correlation is $\mathrm{corr}(S,K) = 1/\sqrt{N}$, the closed forms should degrade predictably as $N$ shrinks; a $1/\sqrt{N}$ correction term to the independence approximation could extend the formulas to the small-array regime where the paper's own $N > 9$ claim does not apply.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper analyzes a downlink MIMO ISAC network with random Rayleigh fading channels and a uniformly distributed target angle, subject to an external communication eavesdropper, a strong or weak sensing eavesdropper, and a malicious-target scenario. The authors propose two closed-form precoding strategies, SSJB and SLB, and derive stochastic sensing metrics (CRB outage probability, ergodic CRB at the BS and at sensing eavesdroppers) and ergodic secrecy rate expressions, including exact formulas for the SSJB external-eavesdropper and malicious-target leakage rates. The results are used to plot CRB-secrecy-rate tradeoff regions and to compare the two precoders.

Significance. The paper targets a timely problem, and the exact SSJB eavesdropper-rate derivations (Lemmas 11 and 12) are clean and correct under the stated model; the two closed-form precoders and the explicit tradeoff discussion are useful contributions if the underlying stochastic metrics are sound. However, the central CRB results are currently tied to a truncated proxy of the advertised ergodic CRB, and several SLB secrecy-rate results are approximations whose accuracy is not quantified. The manuscript is therefore a promising framework that needs substantial revision before its headline claims can be accepted.

major comments (3)
  1. [Section VIII, Lemma 8, Appendix F] The claimed 'ergodic CRB' is not defined for the stated angle model. Under theta ~ U(-pi/2, pi/2), every CRB expression contains a factor 1/cos^2(theta) or 1/cos^2(phi) (e.g., the LCRB in Appendix B and Lemma 4), so E[CRB(theta)] = integral (1/pi) CRB(theta) dtheta diverges because the integrand behaves as sec^2(theta) near +/- pi/2. Appendix F explicitly truncates the domain to [-pi/2+delta, pi/2-delta] and uses E[1/cos^2(theta)] = 2 cot(delta)/(pi-2 delta). Consequently, Lemma 8 and all ergodic-CRB values in Figs. 3 and 4 are expectations of a delta-dependent truncated proxy, not of the 'ergodic CRB' named in the abstract and Section II-A. This is a definitional problem, not a finite-sample or Monte Carlo issue. The authors should either rename the metric throughout (e.g., 'delta-truncated ergodic CRB' with delta=0.1) or replace the uniform angle model with a bounded distribution and re-derive the corresponding formulas.
  2. [Appendix B, Appendix F, Section X] The stochastic closed forms rely on a trivariate CLT approximation for (R,T,K) and, in Appendix F, on the additional approximation that S = R^2+T^2 is independent of K and distributed as N*Exp(1) while K ~ N(N,N). In the true model, S and K are correlated with a correlation that decays only as N^{-1/2}, which is not negligible at the paper's default N=15. The statement in Appendix B that 'for N > 9, the multidimensional CLT holds' is a self-referential assertion supported only by the paper's own Monte Carlo, and no error bound or quantitative accuracy criterion is provided. Because the CRB approximations contain the term 1/(K - S/N), this approximation directly affects the claimed tradeoff curves. The authors should explicitly label all such results as CLT-based approximations and provide a quantitative accuracy check, or supply a rigorous finite-N error bound.
  3. [Lemma 14 and its proof] The SLB ergodic rate at the communication eavesdropper is obtained by replacing E[log(1+SINR)] with log(1+E[SINR]) and then approximating E[SINR] by the ratio of expectations of the numerator and denominator. The proof steps are not justified for an ergodic rate, since Jensen's inequality gives only an inequality and the ratio-of-expectations is an uncontrolled approximation. This formula is used in the SLB secrecy-rate contours of Fig. 2 and the tradeoff regions of Fig. 4, so the SLB ESR is not derived at the same level of rigor as the SSJB exact results. The approximation status of Lemma 14 should be stated prominently in the contributions section, or an exact expression should be supplied.
minor comments (4)
  1. [Figures 2 and 3] The figure labels contain typos: 'Ergpdic Rate' and 'Ergpdic CRB' should be 'Ergodic Rate' and 'Ergodic CRB'.
  2. [Appendix H heading] The heading for the proof of Lemma 11 reads 'Appendix and H'; this should be 'Appendix H'.
  3. [Lemma 16 proof] The proof of Lemma 16 omits the detailed covariance calculations 'due to space limitations'; since this lemma is load-bearing for every CLT-based approximation, the derivations should be included in a supplementary file or in the appendix text.
  4. [Section VIII, Lemma 9] The notation in Lemma 9 is overloaded: M2(S,K), M3(S,K), and M4(S,K) are introduced without a unified definition, and the 'upper bound', 'lower bound', and 'approximation' variants of M2 are not clearly distinguished in the displayed expressions.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the central derivations are self-contained; the ergodic-CRB figures rest on a truncated-domain proxy, which is a correctness concern rather than a circularity.

full rationale

The claimed results are derived, not fitted. CRB(theta) and CRB(phi) follow from the Gaussian FIM (eqs. (1)-(6) and Section III-B); substituting the SSJB/SLB covariance structures (10) and (11) yields Lemmas 2-9. The ESR results are genuinely closed-form: Lemma 11 evaluates E[log(1+SINR_e)] via the chi-square MGF, Lemma 12 uses a^H t1 = alpha sqrt(N) by orthogonality, and Lemmas 13-15 follow the same channel-statistics route. The trivariate-normal approximation (Lemma 16, Appendix B) uses CLT mean mu_d=[0,0,1] and covariance diag(1/2,1/2,1) computed from the Rayleigh/uniform channel statistics, not fitted to the target metrics; Monte Carlo is an independent check. tau, alpha, tau1-tau3 are design parameters swept over, not fitted to reproduce the tradeoffs. Self-citations [1] and [12] motivate the framework (SJB/LB, P(CRB>epsilon)), but the load-bearing derivations are re-derived here and do not reduce to those citations. One non-circular correctness issue: with theta, phi ~ U(-pi/2, pi/2), the CRB is proportional to sec^2, so E[CRB] diverges; Appendix F truncates the domain to [-pi/2+delta, pi/2-delta] with delta=0.1 and reports the truncated expectation as the ergodic CRB, making Figs. 3-4 depend on an arbitrary cutoff. This is a definitional/correctness concern, not a circularity, and it leaves the ESR lemmas unaffected.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central contribution rests on the CLT-based random-vector approximation, the two-stage assumption that the precoder uses the exact target steering vector a(theta) while theta is the estimated parameter, a line-of-sight radar channel model, and the strong-eav threat model in which the sensing spy knows the transmitted signal. Design parameters (tau, alpha, tau1-tau3) and the truncation margin delta are hand-chosen degrees of freedom that determine the reported numeric curves. No invented physical entities are introduced.

free parameters (4)
  • tau (SSJB data power fraction) = swept 0..1 in numerics
    Hand-chosen design parameter splitting power between user data and artificial noise in SSJB; all SSJB metrics are functions of tau.
  • alpha (SSJB user-beam component along target steering vector) = swept 0..1 in numerics
    Controls how much of the user data points at the target; directly sets malicious-target leakage and sensing-eav CRB in SSJB.
  • tau1, tau2, tau3 (SLB power splits for data, AN, radar sr1) = swept, with tau1 + tau2 + tau3 <= 1
    SLB performance (ESR, CRB, outage) is parameterized by these three splits; the 1 - tau1 - tau2 - tau3 remainder goes to radar signal sr2.
  • delta (angle-domain truncation margin for ergodic CRB) = 0.1 rad in numerics
    E[CRB(theta)] and E[CRB(phi)] diverge over the stated uniform angle support because CRB is proportional to 1/cos^2(angle); Appendix F truncates the domain to [-pi/2 + delta, pi/2 - delta], so all reported ergodic CRB values depend on this hand-chosen delta.
assumptions (5)
  • domain assumption Multidimensional CLT: (R, T, K) is trivariate normal N3(N mu_d, N Sigma_d) with mu_d = [0,0,1]^T and Sigma_d = diag(1/2, 1/2, 1); declared valid for N > 9.
    Invoked in Appendix B (Lemma 16) and used in every stochastic metric (Lemmas 2, 3, 5, 7-9, 13, 15). The only support is the paper's own Monte Carlo; no error bound is given, and at finite N, K is Gamma(N,1), not Gaussian.
  • domain assumption S = R^2 + T^2 and K are independent, with S ~ N*Exp(1) and K ~ N(N, N) truncated to K > 0.
    Appendix F writes the joint PDF of S and K as a product of marginals. For finite N the true S and K are correlated (corr(S,K) = 1/sqrt(N) for Gaussian channels), so independence is an approximation that appears exact only in the CLT limit.
  • domain assumption The precoder X is built from the exact target steering vector a(theta) (and a'(theta) in SLB) while theta is the parameter being estimated.
    Section II-A: the BS obtains 'coarse estimates of parameters from a previous stage' (citing [23], [25]) and treats X as fixed in the CRB and rate evaluation. An imperfect angle estimate in the precoder would change every derived expression, including the CRB in Lemma 2.
  • domain assumption Line-of-sight sensing model: yt = c5 a(theta)^H X + zt and echoes Yr = c3 b(theta)a(theta)^H X + Zr, with theta and phi independent and uniform on (-pi/2, pi/2).
    Section II: the radar channel is a rank-1 steering-vector structure with no fading on the sensing paths; this structure drives the orthogonality identities (a^H a' = 0) and the closed forms. The paper claims flexibility to other angle distributions but analyzes only the uniform case.
  • domain assumption The strong sensing eav knows the transmitted signal X (user data su and AN), while the external communication eav does not.
    Section VI assumes the strong eav 'knows su and V'. This is a standard ISAC-privacy upper-bound adversary model, but it is in tension with the data being confidential: an adversary that knows su would trivially intercept the communication. The coexistence of both assumptions is a modeling choice, not a derivation.

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Pith. "Pith review of Secure Integrated Sensing and Communication Networks: Stochastic Performance Analysis." pith.science (2026). https://pith.science/paper/A7GFNU3V

@misc{pith2026250723234,
  author       = {Pith},
  title        = {Pith review of: Secure Integrated Sensing and Communication Networks: Stochastic Performance Analysis},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/A7GFNU3V}},
  note         = {Machine review of arXiv:2507.23234}
}
read the original abstract

This paper analyzes the stochastic security performance of a multiple-input multiple-output (MIMO) integrated sensing and communication (ISAC) system in a downlink scenario. A base station (BS) transmits a multi-functional signal to simultaneously communicate with a user, sense a target's angular location, and counteract eavesdropping threats. The attack model considers a passive single-antenna communication eavesdropper intercepting communication data, as well as a multi-antenna sensing eavesdropper attempting to infer the target's location. We also consider a malicious target scenario where the target plays the role of the communication eavesdropper. The BS-user and BS-eavesdroppers channels follow Rayleigh fading, while the target's azimuth angle is uniformly distributed. To evaluate the performance in this random network, we derive the ergodic secrecy rate (ESR) and the ergodic Cramer-Rao lower bound (CRB), for target localization, at both the BS and the sensing eavesdropper. This involves computing the probability density functions (PDFs) of the signal-to-noise ratio (SNR) and CRB, leveraging the central limit theorem for tractability. We characterize the boundary of the CRB-secrecy rate region, and interpret the performance tradeoffs between communication and sensing while guaranteeing a level of security and privacy in the random ISAC networks.

Figures

Figures reproduced from arXiv: 2507.23234 by the authors.

Figure 1
Figure 1. System model.Ysri and hei denotes the i-th row and element of Ysr and he, respectively conference paper [1], we proposed the SSJB scheme. In this extended work, we now introduce both SSJB and SLB, and significantly enhance the threat model by considering not only external communication eaves but also malicious targets. Furthermore, we account for both weak and strong sensing eaves, whereas the previous work consider… view at source ↗
Figure 2
Figure 2. Ergodic rates vs. BS power coefficients: SLB ( [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. Ergodic CRBs vs. BS power coefficients: SLB ( [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: trade off regions of ESR versus ergodic CRB [PITH_FULL_IMAGE:figures/full_fig_p012_4.png]

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Pith tools

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